Contribution of HIV-1 genomes that do not integrate to the basic reproductive ratio of the virus

Abstract

Recent experimental data indicate that HIV-1 DNA that fails to integrate (from now on called uDNA) can by itself successfully produce infectious offspring virions in resting T cells that become activated after infection. This scenario is likely important at the initial stages of the infection. We use mathematical models to calculate the relative contribution of unintegrated and integrated viral DNA to the basic reproductive ratio of the virus, R0, and the models are parameterized with preliminary data. This is done in the context of both free virus spread and transmission of the virus through virological synapses. For free virus transmission, we find that under preliminary parameter estimates, uDNA might contribute about 20% to the total R0. This requires that a single copy of uDNA can successfully replicate. If the presence of more than one uDNA copy is required for replication, uDNA does not contribute to R0. For synaptic transmission, uDNA can contribute to R0 regardless of the number of uDNA copies required for replication. The larger the number of viruses that are successfully transmitted per synapse, however, the lower the contribution of uDNA to R0 because this increases the chances that at least one virus integrates. Using available parameter values, uDNA can maximally contribute 20% to R0 in this case. We argue that the contribution of uDNA to virus reproduction might also be important for continued low level replication of HIV-1 in the presence of integrase inhibitor therapy. Assuming a 20% contribution of uDNA to the overall R0, our calculations suggest that R0=1.6 in the absence of virus integration. While these are rough estimates based on preliminary data that are currently available, this analysis provides a framework for future experimental work which should directly measure key parameters.

Keywords: HIV dynamics; Unintegrated HIV; Virus dynamics.

Figure 1

Schematic of free virus and synaptic transmission modes. (a) In free virus transmission, viruses are released by an infected cell (grey) and can enter the target cell population. Different virus fates are shown with different target cells. Clockwise from the top: a single virus infects the target cell but remains unintegrated, a single virus infects a target cell and is integrated into the genome, multiple viruses infect a target cell but all remain unintegrated, and multiple viruses infect a target cell and some become integrated. (b) Synaptic transmission potentially involves a high number of viruses transferring into a target cell at once. These viruses can be integrated into the genome or remain unintegrated. In contrast to free virus transmission, the multiplicity of infection can be much higher. A single infected cell can potentially transmit via both modes of transmission.

Figure 2

Fraction contribution to R₀ by cells with uDNA-only for synaptic transmission. Lines are different distributions of the number of viruses transferred per synapse. The contribution to R₀ by uDNA depends on average number of viruses transmitted but remains relatively constant with respect to the distribution of viruses transmitted. We assume that viruses integrate independently. Parameters are λ =10000, d=0.01, η=0.25, p=0.5, c=1, a_i=0.7, a_u=0.7.

Figure 3

(left) Contribution of uDNA towards R₀ for synaptic transmission with varying threshold number of uDNA copies required for productive infection, c. (right) Contribution of uDNA towards R₀ for synaptic transmission with varying integration probabilities, p. We assume that viruses integrate independently and number of viruses transmitted follows a Poisson distribution. Default parameters are λ =10000, d=0.01, η=0.25, p=0.5, c=1, a_i=0.7, a_u=0.7.